Enumeration of Hybrid Domino-Lozenge Tilings

2013/09/20 by Tri Lai, Lai, Tri
Mathematics · #05A15 #05E99 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:05E99

paper · pdf · doi:10.48550/arxiv.1309.5376

35 pages, 31 figures

arxiv created 2013/09/20 · arxiv updated 2013/09/24

Abstract

We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas' Theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.

Related

• Enumeration of Hybrid Domino-Lozenge Tilings III: Centrally Symmetric\n Tilings
• Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-octagonal regions
• A new proof for the number of lozenge tilings of quartered hexagons
• An overview of domino and lozenge tilings
• Enumeration of lozenge tilings of a hexagon with a maximal staircase and\n a unit triangle removed